The Determinants of the Money Supply

The money multiplier, reserve and currency ratios, and borrowed reserves

M1 and the Monetary Base• Recall our definition of M1 as currency in circulation plus

checkable deposits• Recall our definition of MB as currency in circulation plus

reserves

• The Fed has greater control over MB than it does over M1– Checkable deposits are influenced by a number of factors that

the Fed does not have direct control over.

• We link MB and M1 together through the money multiplier– M1 = m*MB– For every $1 increase in the MB, the money supply (M1)

increases by m*$1– m is almost always greater than 1.

The Currency Ratio• How much currency does the public hold

relative to their checkable deposits?– We assume that the desired level of currency

(C) is a constant fraction of checkable deposits

– The currency ratio is a constant (in equilibrium) defined as:

• c = C/D

– C can change, but only in constant proportion to D

Reserve Ratios• What fraction of checkable deposits do banks hold in

reserve?– Banks are required by the Fed to hold a minimum fraction in

reserve defined as the reserve requirement ratio (rr)– Banks may choose to hold excess reserves (i.e. a fraction of

deposits held in reserve above and beyond the minimum required by the fed).

• Let RR be the required reserves held by banks– RR = rr*D, where rr is a parameter set by the Fed

• Let ER be the excess reserves held by banks– ER = e*D, where e is assumed to be a constant proportion set

by banks

• Total reserves (R) = RR + ER = rr*D + e*D = (rr+e)*D– Note that we have been assuming so far that ER=0 (i.e. the

reserve requirement is binding).

Deriving the Money Multiplier• We define MB as currency (C) plus reserves (R)

• Using our definitions:– MB = C + R

– MB = c*D + rr*D + e*D– MB = (rr + e + c)*D

• The monetary base is equal to the fraction of deposits allocated to required reserves, excess reserves, and currency in circulation

Deriving the Money Multiplier

• MB = (rr + e + c)*D

• Rearranging gives:

• Recall M1 = C + D = (c*D) + D = (1+c)*D

• Plugging in our definition of D:

• Since M1 = m*MB:

MBcerr

D++

= 1

MBcerr

c

+++= 1

M1

cerr

c

+++= 1

m

The Money Multiplier• The money multiplier is defined as:

m = (1+c)/(rr+e+c)

• If no currency is held and banks hold no excess reserves, then the money multiplier is simply the inverse reserve ratio– A 10% rr will produce a multiplier of 10– A 20% rr will produce a multiplier of 5

• In reality, people do hold currency and banks do hold excess reserves.

• As a result, the banking system is limited in the amount of money it creates through fractional reserve banking (i.e. multiple deposit creation)– Money held as currency or in reserve is not being loaned out.

Example 1• Suppose the desired currency ratio is 40%, the

reserve requirement is 10% and the excess reserve ratio is 0.5%

• The money multiplier is – m = (1+0.4)/(0.1 + 0.4 + 0.005) = 2.77– A one dollar increase in the monetary base will lead to

a $2.77 increase in the money supply

• Note that if c = e = 0, then the money multiplier would have been 10.

• Accounting for currency and excess reserves is clearly important.

Example 2• Let c = 0.25, e = 0.001, and rr = 0.1.

Compute the money multiplier– m = (1+0.25)/(0.1+0.001+0.25) = 3.56

• The Fed decides to increase rr to 20%. What happens to the money multiplier (and the money supply as a result?)– m = 1.25/0.456 = 2.74– A smaller multiplier means that banks create

less money through lending and therefore the money supply will fall.

Example 3• What happens to the money multiplier when the

desired currency ratio rises?

• Let c = 0.2, rr = 0.25, and e = 0.05– m = (1+0.2)/(0.25+0.05+0.2) = 1.2/0.5 = 2.4

• Now suppose c rises to 0.3, while all other variables remain constant– m = (1+0.3)/(0.25+0.05+0.3) = 1.3/0.6 = 2.17

• Increasing the fraction of deposits held as currency causes the money supply to fall– Money is being taken out of the banking system

where it could have been used to make loans.

Factors that Determine the Money Multiplier

• Changes in the required reserve ratio r– The money multiplier and the money supply are

negatively related to r

• Changes in the currency ratio c– The money multiplier and the money supply are

negatively related to c

• Changes in the excess reserves ratio e– The money multiplier and the money supply are

negatively related to the excess reserves ratio e

Changes in the Currency Ratio

• We have assumed that the constant currency ratio is an independent parameter for simplicity.

• A more complete analysis would examine the factors that cause c to change.– Changes in income/wealth

• Larger proportions of currency are held by people with low income/wealth

• As income/wealth rises, the ratio of currency to deposits falls

– Changes in expected returns• As the interest rate on deposits rises, c falls• As the cost of acquiring currency falls, c rises• Fears of bank insolvency (i.e. bank panics) cause c to rise

sharply• Increases in illegal activity cause c to rise

The Currency Ratio Over Time

ATM’s lower the cost of acquiring currency

Series of bank panics

Increased illegal drug

trade

Big tax increases

Changes in the Excess Reserve Ratio• What are the costs and benefits to banks of holding

excess reserves?

• Market Interest Rates (-)– Every dollar held as an excess reserve has an opportunity cost

equal to the interest rate it could have earned as a bank loan– As market interest rates rise, this opportunity costs increases

and banks hold fewer excess reserves– e is negatively related to market interest rates

• Expected Deposit Outflows (+)– The main benefit of holding excess reserves is that they insulate

the bank (somewhat) from sudden deposit outflows– With excess reserves, banks do not have to call in loans, sell off

other assets, or borrow from the Fed to cover deposits being withdrawn

– If banks think that deposit outflows will increase, they would be wise to increase their excess reserve ratio

– e is positively related to expected deposit outflows.

Excess Reserves and Market Interest Rates

The Decline of the Reserve Ratio as a Policy Tool

• The preceding analysis suggests that the Fed can increase/decrease the money supply by lowering/raising the reserve ratio.– While the Fed used this policy tool in the past, it has become

ineffective in the past decade or so.

– The Fed allows banks to classify some of their membership deposits at the Fed as required reserves

– Banks have found that they need to keep extra currency in ATM’s over weekends and holidays. This currency is classified as vault cash and counts toward required reserves

• With these two developments, banks actually hold more reserves than the minimum required by the Fed

• If rr is not binding, then any change in rr will have little to no effect. (only works if you significantly increase rr!)

• Open market operations are controlled by the Fed, but the Fed does not directly control the amount of borrowing by banks from the Fed

• We split the monetary base into two components, the non-borrowed monetary base (MBn) and borrowed reserves by banks (BR) – MBn= MB – BR MB = MBn + BR

– M1 = m*MB = m*(MBn + BR)

• The money supply increases with both the non-borrowed base and with borrowed reserves– An increase in BR frees up more bank deposits for loans

– BR tends to be very small since the Fed keeps the discount rate above the market interest rate.

Borrowed Reserves

Factors that Change the Money Supply

Changes in the Money Supply, 1980-2006

Explains long run movements

Explains short run fluctuations

• The model we have developed here can be used to explain the sharp reduction in the money supply during the Great Depression– Prior to FDIC, there was no publicly provided insurance for bank deposits

– With the Great Depression, many bank loans failed

– People worried (rightfully) that their bank did not have enough in reserves to cover all deposits

– They rushed to their bank to withdraw their money while their was still something left in reserve

– This sparked a series of bank panics where even financially stable banks were affected

• These bank panics directly led to a reduction in the money supply, even though the Fed would have actually preferred an increase in M1 at this time– Fears of bank insolvency caused c to rise

– Increases in expected deposit outflows caused e to rise

– The multiplier declined sharply

The Bank Panics of the Great Depression

Currency and Excess Reserve Ratios During the Great Depression

M1 and MB during the Great Depression